June 2007 - Sec 1 - Game 1 - Q3

Moving on to Question 3, If the third digit of an acceptable product code is not 0, which

one of the following must be true?

Again, we have two possibilities here. We're saying that the third digit is not 0. So drawing

out two possibilities.

In Scenario 1 our options for the third spot are 0 and 3. If it's not 0 it's going to be

3. Since the fifth digit must be greater than the third digit, or the third digit must be

less than the value of the fifth digit, we know that 4 must be fifth. We know 1 and 2

would be first and second, which puts 0 in four.

What about for option 2? In option 2 our options for the third spot are 0 and 1. The stem from

Question 3 is telling us it's not 0 so it must 1. We know 2 and 4 now are going to be

first and second. We know that the third digit is less than the value of the fifth digit.

The only 2 digits remaining are 0 and 3, which means 3 has to go fifth and 0 comes fourth.

Again, we're looking for what must be true. So Let's take a look:

(A), the second digit of the product code is 2. That's definitely possible in our

first scenario, but it doesn't have to be true because in scenario 2 the second digit

is 4. So (A) is not necessarily true and (A) is out.

(B), the third digit of the product code is 3. In scenario 1 that's true, but in

scenario 2 it's 1, so (B) doesn't have to true and (B) is out.

(C), the fourth digit of the product code is 0. You notice, in both of our scenarios

here, 0 is the fourth digit. (C) must be true and (C) would be the correct answer.